Home-price appreciation is accelerating in much of the U.S., offering the latest confirmation that the housing market is turning after the most severe property downturn since the Great Depression.

Prices rose by 8.1% in January from a year earlier, the largest such gain in 6½ years, according to figures from the S&P/Case-Shiller index of home prices in 20 major metropolitan cities released Tuesday. All 20 cities posted annual increases.